David Swigon
Associate Professor
Department of Mathematics
Alfred P. Sloan Fellow
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University of Pittsburgh
Department of Mathematics
511 Thackeray Hall
Pittsburgh, PA 15260
swigon@pitt.edu
Tel: (412) 624-4689
Fax: (412) 624-8397
My research interests are in the area of applied mathematics with emphasis on mathematical biology. In particular, I work on the design and analysis of mathematical models of biological systems within the framework of theories of continuum mechanics, dynamical systems, and stochastic dynamics.
Inverse problem for ODE models
The utility of any mathematical model is crucially dependent on how well such a model represents the reality. Scientists use various mathematical and statistical tools to make the connection between observed data and model behavior. I am interested in reserach on fundamental questions associated with parameter inference. With my students and collaborators we have studied the existence and uniqueness of parameters for which models reproduces observed data, inferred parameter distributions for ensemble models of in-host immune response, and computed the maximal uncertainty in the data that can be tolerated for a model to predict a robust type of behavior. Our current research is focused on quantifying the uncertainty of model predictions.
Mathematical Immunology
I am interested in the development of mathematical models of in-host human immune response to viral and bacterial infections, and in the relation between immunity and inflammation. With my collaborators we have developed an ODE model for individual response to influenza virus infections and an ensemble model capable of characterizing probabilistic outcomes of treatment scenarios. We have also developed a model of bacterial pneumonia and analyzed the dependence of the observed behavior on the characteristics of the host and bacterial strains.
DNA mechanics
My current projects include the development micromechanical models of
DNA elasticity that combine
atomic-scale and continuum mechanics approaches with recent advances in
computational chemistry and employ information obtained by X-ray
crystallography, single-molecule manipulation, and other experimental
techniques. Part of my research program is oriented towards continuum
modeling of complex macromolecular assemblies and the application of
stochastic and deterministic dynamics in the study of molecular biological processes.
Cell Migration
We are developing a mathematical model of migration of enterocytes during intestinal wound healing process that is based on novel assumption of elastic deformation of the cell layer and incorporates cell mobility, adhesion and proliferation.